Math
posted by Kestrel on .
Determine the values of k for which the function f(x)=4x^23x+2kx+1 has 2 zeros

recall that the formula for discriminant:
D = b^2  4ac
if
D < 0 : two imaginary roots
D = 0 : one root
D > 0 : two real roots
thus, given the equation, we can substitute the values of a, b and c in the discriminant, which must be > 0:
(2k  3)^2  4(4)(1) > 0
4k^2  12k + 9  16 > 0
4k^2  12k  7 > 0
(2k  7)(2k + 1) > 0
these are the ranges of values:
k > 7/2
k < 1/2
hope this helps~ :)